J. Chem. Eng. Data 2004, 49, 631-634
631
Speeds of Sound, Densities, and Isentropic Compressibilities of Poly(propylene glycol)-425 at Temperatures from (293.15 to 373.15) K and Pressures up to 100 MPa Mikhail F. Bolotnikov,* Vyacheslav N. Verveyko, and Marina V. Verveyko Department of General Physic, Kursk State University, Kursk, Radishcheva 33, Russia
Experimental speeds of sound and densities are presented for the liquid phase of poly(propylene glycol)425. The measurements were carried out along nine isotherms from (293.15 to 373.15) K at pressures from saturation condition up to 100 MPa. The speed of sound was measured by a pulse-phase echo ultrasonic device at a frequency of 1 to 5 MHz with an uncertainty of (0.2%. The density was measured by an acoustic piezometer constructed by the authors with an uncertainty of (0.3%. The experimental results were used to calculate isobaric thermal expansion coefficient Rp and isentropic compressibility kS.
Introduction
u)
In recent years, interest to measurement of speed of a sound in heavy organic liquids has considerably increased.1-4 Interest in the properties of poly(propylene glycol) PPG is as a result of their extensive application in the petrochemical, medicine, and pharmaceutical industries. They represent fragments of many surface-active substances and can serve as modeling objects. However, thermodynamic properties of PPG are not clearly understood. Research of these properties was carried out under narrow-range condition parameters. In this work, we report speed of sound and density data for PPG-425 in the range of temperature from (293.15 to 373.15) K at high pressure. To our best knowledge, the speed of sound and density of PPG-425 under high pressures has not been reported.
The speed of sound was measured using a pulse-phase echo ultrasonic device5 at a frequency of (1 to 5) MHz with an uncertainty of (0.2%. Dispersion was not observed. For the simultaneous measurement of speed of sound and density, an acoustic piezometer6 has been developed. This method makes possible measurements of speed of sound and density of a liquid at pressure up to 600 MPa in a temperature range from (223.15 to 523.15) K. The density was measured by the acoustic piezometer with an uncertainty of (0.3%. The acoustic piezometer was thermostated with a temperature stability of (0.01 K. The temperature and pressure were measured by the platinumresistance thermometer and dead-weight pressure gauge MP-2500 with an accuracy of (0.01 K and 0.01 MPa, respectively. Figure 1 shows the acoustic piezometer. The speed of sound was determined by the simple relation should
be
addressed.
E-mail:
(1)
where L is the acoustic path (length of the stationary base) and τ2 and τ1 are the total delay time of the second and the first pulses reflected from the diaphragm, respectively. The variation of acoustic path L with temperature and pressure was calculated from the formula
LP,T ) L0ΩPΩT
(2)
where L0 ) 24.807 mm is the path length at temperature T0 ) 293.15 K and pressure P0 ) 0.1 MPa
ΩT ) 1 + R(T/K - 293) ΩP ) 1 -
Experimental Section
* To whom correspondence
[email protected].
2L τ2 - τ 1
1 - 2µ P E
(3) (4)
where µ, R, E, T, and P are Poisson’s coefficient, coefficient of thermal expansion, Young’s modulus, absolute temperature, and pressure, respectively. The length of the stationary base at temperature T0 ) 293.15 K and pressure P0 ) 0.1 MPa was measured by the device IZV-2 (Russia) with a precision of (0.001 mm. The density was determined by the change of volume at compression of the bellows (eq 1). Change of length of the bellows (moving of the reflector 11) was registered on speed of sound. According to Bridgman,7 the change of volume of the bellows at compression can be determined from
∆V ) S0∆h
(5)
where ∆h is the change of length of the bellows and S0 is the square of the effective cross-section
V ) V0 + S0∆h
(6)
V ) vm
(7)
10.1021/je034212y CCC: $27.50 © 2004 American Chemical Society Published on Web 03/25/2004
632
Journal of Chemical and Engineering Data, Vol. 49, No. 3, 2004 Table 1. Reference Speed of Sound and Density of Pentane at 293.15 K and 313.15 K 293.15 K
where v is specific volume of the liquid, m is the mass of the liquid
v ) v0 +
S0∆h m
(8)
Therefore
F/(kg‚m3)
u/(m‚s-1)
P/MPa
exp
lita
exp
lita
exp
lita
exp
lita
0.1 50 100 150 200 250 300 350 400 450 500 550 600
626.4 666.9 702.8 728.6 748.7 764.8 778.2 790.0 800.7 810.9 820.6 830.0 838.9
626 666 705 730 748 763 779 791 800 811 820 830 840
1029 1357 1568 1731 1878 1989 2104 2197 2294 2381 2469 2534 2606
1030 1356 1569 1730 1879 1991 2105 2196 2292 2380 2469 2535 2608
606.3 653.3 689.6 716.9 737.7 754.0 767.4 779.0 789.6 799.8 809.7 819.5 828.9
606 650 694 717 736 752 768 780 791 800 808 819 830
934 1290 1511 1686 1833 1934 2049 2140 2240 2301 2397 2448 2538
934 1291 1510 1685 1835 1936 2050 2140 2238 2300 2398 2450 2540
a
Figure 1. Acoustic piezometer. 1, bellows; 2, stationary base; 3, piezoelectric ceramics; 4, contact plate; 5, spring; 6, lead-in wire; 7, wire; 8, pressurized body; 9, fluoroplastic gasket; 10, diaphragm; 11, reflectors.
313.15 K
u/(m‚s-1)
F/(kg‚m3)
Reference 9.
pressure Pi, respectively; τ0 and τi are propagation times by ultrasound at distances from the reflector and back at atmospheric pressure P0 and at some pressure Pi, respectively. The initial density at atmospheric pressure P0 was measured by an Ostwald-Sprengel-type pycnometer, with a volume of approximately 50 cm3. The uncertainty of the density measurements was estimated to be (3 × 10-5 g‚cm-3. The effective cross section of the bellows was determined on the basis of measurements of liquid dependence of density on pressure is well known.8 We have compared our results for speed of sound and density with data reported by other authors. The speeds of sound and densities for pentane, at 293.15 K and 313.15 K, were in good agreement with Rasumihin’s9 data (Table 1). The PPG with number-average molecular weights of 425 g‚mol-1 were manufactured by Merck and were used without further purification. The purity of PPG-425 was checked by gel permeation chromatography. The purity of PPG-425 was 99.7 mol %. The including of the water did not exceed 0.1 mol %. A polydispersity index of PPG-425 was 1.086. Experimental values of density and refractive index at 293.15 K of PPG-425 were F ) 1020.1 kg‚m-3 and nD ) 1.4468, respectively. Results and Discussion The experimental results of the speed of sound, u, and density, F, in the liquid phase of PPG-425 at various temperatures, T, and pressures P are listed in Tables 2 and 3 and are plotted as a function of temperature and pressure in Figures 2-5, respectively. The data, which is presented in Tables 2 and 3, have been fitted by the following cubic polynomial for each isotherm
Y ) A0 + A1P/MPa + A2(P/MPa)2 + A3(P/MPa)3 (11) F-1 ) F0-1 +
S0∆h m
(9)
where F0 is the density of liquid at atmospheric pressure, F is the density of liquid at some pressure P, and
∆h ) L0 - L )
u0τ0 - uiτi 2
(10)
where Y is u/m‚s-1 or F/kg‚m-3, P is pressure, and A0, A1, and A2 are adjustable parameters. All the measured data were used in the fitting process. The values of coefficients, Ai, were calculated by the least-squares method. Standard deviation σ(Y) of u and F is defined by n
σ(Y) ) [{
∑ (Y
obs
- Ycal)2}/{(n - p)}]1/2
(12)
i)1
where L0 and L are the distances from a piezoelectric ceramics (eq 3) up to the reflector at atmospheric pressure P0 and at some pressure Pi, respectively; u0 and ui are the speeds of sound at atmospheric pressure P0 and at some
Where Yobs and Ycal are the observed and calculated quantities as defined earlier, n is total number of experimental points, and p is the number of estimated parameters. The
Journal of Chemical and Engineering Data, Vol. 49, No. 3, 2004 633
Figure 2. Speed of sound in the liquid phase of PPG-425 as a function of pressure: [, 293.15 K; 2, 313.15 K; O, 333.15 K; 9, 353.15 K; 4, 373.15 K.
Figure 3. Speed of sound in the liquid phase of PPG-425 as a function of temperature: [, P ) 0.1 MPa; O, P ) 20 MPa; 2, P ) 40 MPa; ×, P ) 60 MPa; 9, P ) 80 MPa; 4, P ) 100 MPa.
values of parameters Ai of eq 11 and standard deviation σ(Y) are given in Tables 4 and 5 at temperatures from (293.15 to 373.15) K, respectively. As can be seen from Figures 2-5, the speed of sound and density for PPG-425 monotonically decrease with an increase in temperature
Figure 4. Density in the liquid phase of PPG-425 as a function of pressure: [, 293.15 K; 2, 313.15 K; O, 333.15 K; 9, 353.15 K; 4, 373.15 K.
Figure 5. Density in the liquid phase of PPG-425 as a function of temperature: [, P ) 0.1 MPa; O, P ) 20 MPa; 2, P ) 40 MPa; ×, P ) 60 MPa; 9, P ) 80 MPa; 4, P ) 100 MPa.
along isobars and increase with increase pressure along isotherms. Values of speed of sound and density both change with temperature and with pressure have nonlinear character pronounced along isotherms. And also, the
Table 2. Speed of Sound, u, in the Liquid Phase for PPG-425 at Various Temperatures, T, and Pressures, P u/(m‚s-1) at T/K P/ MPa
293.15
303.15
313.15
323.15
333.15
343.15
353.15
363.15
373.15
0.1 10 20 30 40 50 60 70 80 90 100
1393 1436 1477 1518 1558 1597 1636 1675 1713 1750 1787
1365 1408 1450 1492 1533 1574 1614 1653 1692 1730 1768
1335 1379 1423 1466 1508 1550 1591 1631 1671 1710 1748
1304 1350 1395 1439 1483 1526 1568 1609 1649 1689 1728
1272 1320 1367 1412 1457 1501 1544 1586 1627 1668 1707
1240 1290 1338 1384 1431 1476 1520 1562 1604 1646 1686
1207 1258 1308 1356 1404 1450 1495 1538 1581 1623 1664
1173 1226 1277 1327 1376 1423 1469 1513 1557 1600 1642
1138 1193 1246 1297 1347 1395 1442 1488 1533 1576 1619
Table 3. Density, G, in the Liquid Phase for PPG-425 at Various Temperatures, T, and Pressures, P F/(kg‚m3) at T/K P/ MPa
293.15
303.15
313.15
323.15
333.15
343.15
353.15
363.15
373.15
0.1 10 20 30 40 50 60 70 80 90 100
1020 1026 1031 1036 1041 1046 1050 1054 1058 1061 1064
1012 1018 1024 1029 1034 1039 1043 1047 1051 1055 1058
1005 1011 1016 1022 1027 1032 1037 1041 1045 1049 1052
996 1003 1009 1015 1021 1026 1031 1035 1039 1043 1046
988 995 1001 1008 1013 1019 1024 1028 1032 1036 1040
979 986 993 1000 1006 1012 1017 1021 1025 1029 1033
970 978 985 992 998 1004 1009 1014 1018 1022 1026
962 969 977 984 990 996 1001 1006 1011 1015 1019
953 961 968 976 982 988 994 999 1004 1008 1012
634
Journal of Chemical and Engineering Data, Vol. 49, No. 3, 2004
Figure 6. Pressure dependence, P, of isentropic compressibilities, kS, in the liquid phase of PPG-425: [, 293.15 K; 2, 313.15 K; O, 333.15 K; 9, 353.15 K; 4, 373.15 K. Table 4. Values of the Parameters of Eq 11 and Standard Deviation for Speed of Sound from (293.15 to 373.15) K T/K 293 303 313 323 333 343 353 363 373
A0 1392.95 1364.64 1334.58 1303.62 1271.77 1239.75 1206.45 1172.47 1137.68
A1 4.2908 4.3435 4.4832 4.6554 4.8506 5.0397 5.2263 5.4191 5.5973
A2
σ/m‚s-1
A3 10-3
-4.5294 × -3.3042 × 10-3 -3.5642 × 10-3 -4.3565 × 10-3 -5.6681 × 10-3 -7.0632 × 10-3 -7.8678 × 10-3 -9.2279 × 10-3 -1.0006 × 10-2
10-5
1.0430 × 1.9417 × 10-6 8.6123 × 10-7 2.3164 × 10-6 7.0761 × 10-6 1.3014 × 10-5 1.3537 × 10-5 1.9862 × 10-5 2.1692 × 10-5
1.09 0.64 0.53 0.65 0.93 1.54 0.78 0.83 0.84
Table 5. Values of the Parameters of Eq 11 and Standard Deviation for Density from (293.15 to 373.15) K T/K
A0
A1
293 303 313 323 333 343 353 363 373
1020.10 1011.94 1005.00 995.97 987.82 978.59 969.92 961.65 952.91
0.5650 0.6352 0.5809 0.7021 0.7340 0.7995 0.8279 0.8218 0.8230
A2
A3
-8.2609 × 10-4 -4.3475 × 10-6 -2.2343 × 10-3 5.0315 × 10-6 -4.9718 × 10-4 -6.0768 × 10-6 -2.0543 × 10-3 4.1000 × 10-7 -2.5377 × 10-3 3.9337 × 10-6 -3.0433 × 10-3 4.5753 × 10-6 -3.3152 × 10-3 6.3094 × 10-6 -3.0390 × 10-3 5.5543 × 10-6 -2.3534 × 10-3 2.8624 × 10-7
σ/kg‚m-3 0.60 0.58 0.65 0.63 1.14 1.17 0.53 0.77 0.70
maximal change of speed of sound and density values at change of pressure and temperatures occurs in the range of small pressure and high temperatures. Isentropic compressibilities kS of the PPG-425 were calculated from the Laplace equation
kS )
1 Fu2
(13)
where u is the sound velocity and F is the density. The values of isentropic compressibilities kS for PPG-425 as a function of pressure at constant temperatures are plotted in Figure 6. The isobaric thermal expansion coefficient
RP ) -
1 ∂F F ∂T
( )
P
(14)
was calculated from numerical differentiation of the density fitting equation. In Figure 7 is given the isobaric thermal expansion coefficient Rp for the PPG-425 as a function of
Figure 7. Pressure dependence, P, of the isobaric thermal expansion coefficient, RP, in the liquid phase of PPG-425: [, 293.15 K; 2, 313.15 K; O, 333.15 K; 9, 353.15 K; 4, 373.15 K.
pressure at constant temperatures. The uncertainties of the calculated values are not greater than (1% for isentropic compressibility kS and (5% for isobaric thermal expansion coefficient Rp, respectively. Conclusions Speeds of sound and densities are presented for the PPG425 at temperatures from (293.15 to 373.15) K and pressures up to 100 MPa. An acoustic piezometer described in the submitted work has allowed us to obtain the speed of sound and density data with the uncertainty of (0.2% and (0.3%, respectively. These dates are a small part of our research program of systematic investigations of thermodynamic properties for organic liquids. Literature Cited (1) Dutor, S.; Lagourette, B.; Daridon, J. L. High-Pressure Speed of Sound, Density and Compressibility of Heavy Normal Paraffins: C28H58 and C36H74. J. Chem. Thermodyn. 2002, 34, 475-484. (2) Lopez, E. R.; Daridon, J. L.; Baylaucq, A.; Fernandez, J. Thermophysical Properties of Two Poly(alkylene glycol) Derivative Lubricants from High-Pressure Acoustic Measurements. J. Chem. Eng. Data 2003, 48, 1208-1213. (3) Daridon, J. L.; Carrier, H.; Lagourette, B. Pressure Dependence of the Thermophysical Properties of n-Pentadecane and nHeptadecane. Int. J. Thermophys. 2002, 23, 697-708. (4) Daridon, J. L.; Lagrabette, A.; Lagourette, B. Thermophysical Properties of Heavy Synthetic Cuts from Ultrasonic Speed Measurements under Pressure. J. Chem. Thermodyn. 1998, 30, 607-623. (5) Bolotnikov, M. F.; Neruchev, Yu. A. Speed of Sound of Hexane + 1-Chlorohexane, Hexane + 1-Iodohexane, and 1-Chlorohexane + 1-Iodohexane at Saturation Condition J. Chem. Eng. Data 2003, 48, 411-415. (6) Verveyko, V. N.; Mel’nikov, G. A.; Tutov, V. M.; Otpushchennikov, N. F. Research of Organic Liquids with Help Acoustic Piezometer. Ul’trazvuk Termodin. Svoistva Veshchectva 1987, 86-95. (7) Bridgman, P. W. Recent Work in the Field of High Pressures. Rev. Mod. Phys. 1946, 18, 1-93. (8) Cibulka, I.; Takagi, T. P-F-T Data of Liquids: Summarization and Evaluation. 5. Aromatic Hydrocarbons. J. Chem. Eng. Data 1999, 44, 411-429. (9) Razumihin, V. N. The Hydrostatic Method of Determining the Density of Liquids under Pressures Up To 5000 kg/sq. cm. Tr. Vses. Nauchno-Issled. Inst. Fiz.-Tekh. Radiotekh. Izmer. 1960, 46, 96-107.
Received for review October 27, 2003. Accepted February 23, 2004.
JE034212Y
